First-principles formulation of high-energy radiation from magnetar giant flares

We develop a first-principles atmosphere model for neutron stars with ultra-strong magnetic fields ($B\sim {10}^{14},G$). In this framework, a magnetar giant flare (MGF) arises when a large energy release into confined field lines launches an expanding fireball (FB); thermal photons from the FB are Comptonized by relativistic $e^{\pm }$ pairs, producing a modified blackbody spectrum with a Rayleigh–Jeans low-energy slope and a high-energy tail. We derive polarization-dependent opacities for a magnetized $e^{\pm }$ pair plasma (including plasma and vacuum polarization effects) and formulate the coupled radiative-transfer equations for the ordinary and extraordinary modes. The calculations show that, in deep magnetospheric layers with $n\sim {10}^{24}$–${10}^{28},c{m}^{-3}$ and path length $l\sim {10}^3$–${10}^6,\mathrm{cm}$, plasma effects substantially reshape the opacities and generate a broad spectral feature ($\Delta \omega /\omega$) around the electron cyclotron frequency ${\omega }_B$ via resonant polarization/mode conversion. Identifying this feature in data would enable a direct estimate of the surface magnetic field. Despite current observational limitations, the model reproduces key spectral properties of GRB200415A and GRB231115A, providing insight into their radiation mechanisms and the emission physics of MGFs.